Higher Forms of Reasoning.
The two higher forms of reasoning are known, respectively, as (1) inductive reasoning, or inference from particular facts to general laws; and (2) deductive reasoning, or inference from general truths to particular truths. While the class distinction is made for the purpose of clear consideration, it must not be forgotten that the two forms of reasoning are generally found in combination. Thus, in inductive reasoning many steps are taken by the aid of deductive reasoning; and, likewise, before we can reason deductively from general truths to particular ones we must have discovered the general truths by inductive reasoning from particular facts. Thus there is a unity in all reasoning processes as there is in all mental operations. Inductive reasoning is a synthetical process; deductive reasoning, an analytical one. In the first we combine and build up, in the latter we dissect and separate.
CHAPTER XXVI.
Inductive Reasoning.
INDUCTIVE reasoning is based upon the axiom: "What is true of the many is true of the whole." This axiom is based upon man's belief in the uniformity of nature. Inductive reasoning is a mental ladder by which we climb from particular facts to general laws, but the ladder rests upon the belief that the universe is governed by law.
The steps in inductive reasoning are as follows:—
I. Observation, investigation, and examination of particular facts or things. If we wish to know the general characteristics of the bird family, we must first examine a sufficient number of birds of many kinds so as to discover the comparatively few general characteristics possessed by all of the bird family, as distinct from the particular characteristics possessed by only some of that family. The greater the number of individuals examined, the narrower becomes our list of the general qualities common to all. In the same way we must examine many kinds of flowers before we come to the few general qualities common to all flowers, which we combine in the general concept of "flower." The same, of course, is true regarding the discovery of general laws from particular facts. We examine the facts and then work toward a general law which will explain them. For instance, the Law of Gravitation was discovered by the observation and investigation of the fact that all objects are attracted to the earth; further investigation revealed the fact that all material objects are attracted to each other; then the general law was discovered, or, rather, the hypothesis was advanced, was found to explain the facts, and was verified by further experiments and observation.
II. The second step in inductive reasoning is the making of an hypothesis. An hypothesis is a proposition or principle assumed as a possible explanation for a set or class of facts. It is regarded as a "working theory," which must be examined and tested in connection with the facts before it is finally accepted. For instance, after the observation that a number of magnets attracted steel, it was found reasonable to advance the hypothesis that "all magnets attract steel." In the same way was advanced the hypothesis that "all birds are warm-blooded, winged, feathered, oviparous vertebrates." Subsequent observation and experiment established the hypothesis regarding the magnet, and regarding the general qualities of the bird family. If a single magnet had been found which did not attract steel, then the hypothesis would have fallen. If a single bird had been discovered which was not warm-blooded, then that quality would have been stricken from the list of the necessary characteristics of all birds.
A theory is merely an hypothesis which has been verified or established by continued and repeated observation, investigation, and experiment.
Hypotheses and theories arise very frequently from the subconscious assimilation of a number of particular facts and the consequent flashing of a "great guess," or "sacred suspicion of the truth," into the conscious field of attention. The scientific imagination plays an important part in this process. There is, of course, a world of difference between a "blind guess" based upon insufficient data and a "scientific guess" resulting from the accumulation of a vast store of careful and accurate information. As Brooks says: "The forming of an hypothesis requires a suggestive mind, a lively fancy, a philosophic imagination that catches a glimpse of the idea through the form or sees the law standing behind the fact." But accepted theories, in the majority of cases, arise only by testing out and rejecting many promising hypotheses and finally settling upon the one which best answers all the requirements and best explains the facts. As an authority says: "To try wrong guesses is with most persons the only way to hit upon right ones."
III. Testing the hypothesis by deductive reasoning is the third step in inductive reasoning. This test is made by applying the hypothetical principle to particular facts or things; that is, to follow out mentally the hypothetical principle to its logical conclusion. This may be done in this way: "If so and so is correct, then it follows that thus and so is true," etc. If the conclusion agrees with reason, then the test is deemed satisfactory so far as it has gone. But if the result proves to be a logical absurdity or inconsistent with natural facts, then the hypothesis is discredited.
IV. Practical verification of the hypothesis is the fourth step in inductive reasoning. This step consists of the actual comparison of observed facts with the "logical conclusions" arising from applying deductive reasoning to the general principle assumed as a premise. The greater number of facts agreeing with the conclusions arising from the premise of the hypothesis, the greater is deemed the "probability" of the latter. The authorities generally assume an hypothesis to be verified when it accounts for all the facts which properly are related to it. Some extremists contend, however, that before an hypothesis may be considered as absolutely verified, it must not only account for all the associated facts but that also there must be no other possible hypothesis to account for the same facts. The "facts" referred to in this connection may be either (1) observed phenomena, or (2) the conclusions of deductive reasoning arising from the assumption of the hypothesis, or (3) the agreement between the observed facts and the logical conclusions. The last combination is generally regarded as the most logical. The verification of an hypothesis must be "an all-around one," and there must be an agreement between the observed facts and the logical conclusions in the case—the hypothesis must "fit" the facts, and the facts must "fit" the hypothesis. The "facts" are the glass slipper of the Cinderella legend—the several sisters of Cinderella were discarded hypotheses, the slipper and the sisters not "fitting." When Cinderella's foot was found to be the one foot upon which the glass slipper fitted, then the Cinderella hypothesis was considered to have been proved—the glass slipper was hers and the prince claimed his bride.
CHAPTER XXVII.
Deductive Reasoning.
WE have seen in the preceding chapter that from particular facts we reason inductively to general principles or truths. We have also seen that one of the steps of inductive reasoning is the testing of the hypothesis by deductive reasoning. We shall now also see that the results of inductive reasoning are used as premises or bases for deductive reasoning. These two forms of reasoning are opposites and yet complementary to each other; they are in a sense independent and yet are interdependent. Brooks says: "The two methods of reasoning are the reverse of each other. One goes from particulars to generals; the other from generals to particulars. One is a process of analysis; the other is a process of synthesis. One rises from facts to laws; the other descends from laws to facts. Each is independent of the other, and each is a valid and essential method of inference."
Halleck well expresses the spirit of deductive reasoning as follows: "After induction has classified certain phenomena and thus given us a major premise, we may proceed deductively to apply the inference to any new specimen that can be shown to belong to that class. Induction hands over to deduction a ready-made premise. Deduction takes that as a fact, making no inquiry regarding its truth. Only after general laws have been laid down, after objects have been classified, after major premises have been formed, can deduction be employed."
Deductive reasoning proceeds from general principles to particular facts. It is a descending process, analytical in its nature. It rests upon the fundamental axiomatic basis that "whatever is true of the whole is true of its parts," or "whatever is true of the universal is true of the particulars."
The process of deductive reasoning may be stated briefly as follows: (1) A general principle of a class is stated as a major premise; (2) a particular thing is stated as belonging to that general class, this statement being the minor premise; therefore (3) the general class principle is held to apply to the particular thing, this last statement being the conclusion. (A "premise" is "a proposition assumed to be true.")
The following gives us an illustration of the above process:—
I. (Major premise)—A bird is a warm-blooded, feathered, winged, oviparous vertebrate.
II. (Minor premise)—The sparrow is a bird; therefore
III. (Conclusion)—The sparrow is a warm-blooded, feathered, winged, oviparous vertebrate.
Or, again:—
I. (Major premise)—Rattlesnakes frequently bite when enraged, and their bite is poisonous.
II. (Minor premise)—This snake before me is a rattlesnake; therefore
III. (Conclusion)—This snake before me may bite when enraged, and its bite will be poisonous.
The average person may be inclined to object that he is not conscious of going through this complicated process when he reasons about sparrows or rattlesnakes. But he does, nevertheless. He is not conscious of the steps, because mental habit has accustomed him to the process, and it is performed more or less automatically. But these three steps manifest in all processes of deductive reasoning, even the simplest. The average person is like the character in the French play who was surprised to learn that he had "been talking prose for forty years without knowing it." Jevons says that the majority of persons are equally surprised when they find out that they have been using logical forms, more or less correctly, without having realized it. He says: "A large number even of educated persons have no clear idea of what logic is. Yet, in a certain way, every one must have been a logician since he began to speak."
There are many technical rules and principles of logic which we cannot attempt to consider here. There are, however, a few elementary principles of correct reasoning which should have a place here. What is known as a "syllogism" is the expression in words of the various parts of the complete process of reasoning or argument. Whately defines it as follows: "A syllogism is an argument expressed in strict logical form so that its conclusiveness is manifest from the structure of the expression alone, without any regard to the meaning of the term." In short, if the two premises are accepted as correct, it follows that there can be only one true logical conclusion resulting therefrom. In abstract or theoretical reasoning the word "if" is assumed to precede each of the two premises, the "therefore" before the conclusion resulting from the "if," of course. The following are the general rules governing the syllogism:—
I. Every syllogism must consist of three, and no more than three, propositions, namely (1) the major premise, (2) the minor premise, and (3) the conclusion.
II. The conclusion must naturally follow from the premises, otherwise the syllogism is invalid and constitutes a fallacy or sophism.
III. One premise, at least, must be affirmative.
IV. If one premise is negative, the conclusion must be negative.
V. One premise, at least, must be universal or general.
VI. If one premise is particular, the conclusion also must be particular.
The last two rules (V. and VI.) contain the essential principles of all the rules regarding syllogisms, and any syllogism which breaks them will be found also to break other rules, some of which are not stated here for the reason that they are too technical. These two rules may be tested by constructing syllogisms in violation of their principles. The reason for them is as follows: (Rule V.) Because "from two particular premises no conclusion can be drawn," as, for instance: (1) Some men are mortal; (2) John is a man. We cannot reason from this either that John is or is not mortal. The major premise should read "all men." (Rule VI.) Because "a universal conclusion can be drawn only from two universal premises," an example being needless here, as the conclusion is so obvious.